use a Venn diagram and the given information to n (union) = 103, n (A) = 35, n (B) = 42, n (C) = 45, n (A intersection B) = 8, n (A intersection C) = 8, n (B intersection C) = 6, and n (A intersection (B intersection C) = 3. Find n (A intersection (B union C) '). A) 4 B) 22 C) 3 D) 26

Question

Mathematics

Karlee English

29 March, 04:04

use a Venn diagram and the given information to n (union) = 103, n (A) = 35, n (B) = 42, n (C) = 45, n (A intersection B) = 8, n (A intersection C) = 8, n (B intersection C) = 6, and n (A intersection (B intersection C) = 3. Find n (A intersection (B union C) '). A) 4 B) 22 C) 3 D) 26

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Answers (1)

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Adrienne Fuller · Answer 1

The correct option is B.

Step-by-step explanation:

Given information: n (A) = 35, n (B) = 42, n (C) = 45, n (A∩B) = 8, n (A∩C) = 8, n (B∩C) = 6, and n (A∩B∩C) = 3.

We need to find the value of n (A∩ (B∩C) ')

Using venn diagram we get

n (A∩B∩C') = n (A∩B) - n (A∩B∩C) = 8-3 = 5

n (A∩B'∩C) = n (A∩C) - n (A∩B∩C) = 8-3 = 5

n (A'∩B∩C) = n (B∩C) - n (A∩B∩C) = 6-3 = 3

n (A∩ (B∪C) ') = n (A) - n (A∩B'∩C) - n (A∩B∩C') - n (A∩B∩C)

n (A∩ (B∪C) ') = 35-5-5-3 = 22

The value of n (A∩ (B∪C) ') is 22. Therefore the correct option is B.